Large deviation estimate of transition densities for jump processes (Q1359050)

The author gives asymptotic upper and lower bounds of deviation type for the transition density of a jump type process on \(\mathbb R^d\), which is composed of stable-like processes on the line and vector field on \(\mathbb R^d\). To do this he uses the theory of Malliavin calculus both for diffusion and for jump type processes. In the case where there is no drift, the upper and lower bounds coincide.